U.S. patent application number 09/803271 was filed with the patent office on 2001-10-18 for system and method of generating a high efficiency biphasic defibrillation waveform for use in an implantable cardioverter/defibrillator (icd).
Invention is credited to Fishler, Matthew G., Kroll, Mark W., Mouchawar, Gabriel A..
Application Number | 20010031992 09/803271 |
Document ID | / |
Family ID | 26724123 |
Filed Date | 2001-10-18 |
United States Patent
Application |
20010031992 |
Kind Code |
A1 |
Fishler, Matthew G. ; et
al. |
October 18, 2001 |
System and method of generating a high efficiency biphasic
defibrillation waveform for use in an implantable
cardioverter/defibrillator (ICD)
Abstract
In an ICD, a highly efficient biphasic defibrillation pulse is
generated by switching at least two charged capacitors from a
parallel connection to various combinations of a parallel/series
connection or a series connection during the first phase of the
defibrillation pulse. Such mid-stream parallel/series connection
changes of the capacitors and steps up the voltage applied to the
cardiac tissue during the first phase. A stepped-up voltage during
the first phase, in turn, gives an extra boost to, and thereby
forces additional charge (current) into, the cardiac tissue cells,
and thereby transfers more charge to the membrane of the excitable
cardiac cell than if the capacitors were continuously discharged in
series. Phase reversal is timed with the cell membrane reaching its
maximum value at the end of the first phase.
Inventors: |
Fishler, Matthew G.;
(Ithaca, NY) ; Mouchawar, Gabriel A.; (Newhall,
CA) ; Kroll, Mark W.; (Simi Valley, CA) |
Correspondence
Address: |
PACESETTER, INC.
15900 Valley View Court
Sylmar
CA
91392-9221
US
|
Family ID: |
26724123 |
Appl. No.: |
09/803271 |
Filed: |
March 9, 2001 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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09803271 |
Mar 9, 2001 |
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09073394 |
May 5, 1998 |
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6233483 |
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60046610 |
May 15, 1997 |
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Current U.S.
Class: |
607/5 |
Current CPC
Class: |
A61N 1/3906 20130101;
A61N 1/3912 20130101; A61N 1/3956 20130101 |
Class at
Publication: |
607/5 |
International
Class: |
A61N 001/39 |
Claims
What is claimed is:
1. A method for generating an improved biphasic defibrillation
waveform, comprising the steps of: charging at least two capacitors
to a first voltage; switchably coupling the at least two capacitors
to a patient's heart in one of a parallel, a series or a
parallel/series combination configuration; generating a biphasic
shocking pulse having a positive phase and a negative phase, the
positive phase having a first portion with a first peak voltage
followed by a first time interval and at least a second portion
with second peak voltage followed by at least a second time
interval before being truncated and beginning the negative phase,
the sum of the first and at least the second time intervals
defining a desired pulse width; and determining an optimum duration
for each time interval based on a maximum myocardial cell membrane
potential produced in response to each portion of the positive
phase so that, for the desired pulse width, the shocking pulse
produces a higher final cell membrane potential than a value that
would be achieved if the at least two capacitors were continuously
discharged in series.
2. The method of claim 1, wherein the step of determining the
optimum duration for each time interval comprises the step of:
determining the optimum durations for each time interval based on
the value of the at least two capacitors, a predetermined tissue
time constant, .tau..sub.m, and a predetermined tissue resistance,
R.sub.S.
3. The method of claim 2, further comprising the steps of:
connecting the at least two capacitors in parallel during the first
time interval of the biphasic shocking pulse; and connecting the at
least two capacitors in series during at least the second time
interval of the biphasic shocking pulse.
4. The method of claim 3, wherein the at least two capacitors
includes a first capacitor, C.sub.A, and a second capacitor,
C.sub.B, the method further comprising the steps of: generating,
during the first portion of shocking pulse, a waveform having an
exponential decay defined by a first time constant, .tau..sub.S1,
that varies as a function of the predetermined tissue resistance,
R.sub.S, and the first and second capacitors, C.sub.A and C.sub.B,
in accordance with the formula R.sub.S(C.sub.A+C.sub.B); and
generating, during the second portion of shocking pulse, a waveform
having an exponential decay defined by a second time constant,
.tau..sub.S2, that varies as a function of the predetermined tissue
resistance, R.sub.S, and the first and second capacitors, C.sub.A
and C.sub.B, in accordance with the formula
R.sub.S(C.sub.A.multidot.C.sub.B)/(C.sub.A+C.sub.B).
5. The method of claim 4, wherein: the step of determining the
optimum duration, d.sub.1.sup.opt, for the first time interval
comprises the step of defining: 17 d 1 opt = - m 1 ln { ( m s1 ) (
2 1 - 2 1 - 2 ) } the step of determining the optimum duration,
d.sub.2.sup.opt, for the second time interval comprises the step of
defining: 18 d 2 opt = + m 2 ln { ( 1 2 ) ( 2 1 - 2 1 - 2 ) }
wherein .alpha..sub.1=1-(.tau..sub.m/.tau..sub.S1) and
.alpha..sub.2=1-(.tau..sub.m/.tau..sub.S2); and wherein
.tau..sub.S1=R.sub.S.multidot.(C.sub.A+C.sub.B) and
.tau..sub.S2=R.sub.S.multidot.(C.sub.AC.sub.B)/(C.sub.A+C.sub.B).
6. The method of claim 5, wherein the step of determining the
optimum duration for each time interval comprises the step of:
determining the optimum value for the first and second capacitors,
C.sub.A and C.sub.B, that maximizes the final myocardial cell
membrane potential for a given total stored energy.
7. The method of claim 6, wherein the first and second capacitors,
C.sub.A and C.sub.B, are related by a scaling factor defined by a
relationship k=C.sub.A/C.sub.B, wherein the step of determining the
optimum values for the first and second capacitors, C.sub.A and
C.sub.B, comprises the step of: defining a range for the scaling
factor, k, as being approximately within the range of
0.7<k<1.4 so as to be within approximately 1% of an optimal
energy efficiency for a given .tau..sub.m and R.sub.S.
8. The method of claim 7, wherein the step of determining the
optimum values for the first and second capacitors, C.sub.A and
C.sub.B, comprises the step of: defining the value for capacitor,
C.sub.A, approximately equal to the value for capacitor,
C.sub.B.
9. The method of claim 8, wherein the step of determining the
optimum duration for each time interval comprises the step of:
defining the relationship between the first time constant,
.tau..sub.S1, and the second time constant, .tau..sub.S2, as
.tau..sub.S1=4.multidot..tau..sub.- S2.
10. The method of claim 9, wherein the step of determining the
optimum values for the first and second capacitors, C.sub.A and
C.sub.B, comprises the step of: determining the optimum value for
the first and second capacitors, C.sub.A and C.sub.B, that
minimizes the total stored energy needed for the predetermined
tissue time constant, .tau..sub.m and the predetermined tissue
resistance, R.sub.S.
11. The method of claim 10, wherein the step of determining the
optimum values for the first and second capacitors, C.sub.A and
C.sub.B, comprises the step of: defining a relationship between
C.sub.A+C.sub.B and .tau..sub.m/R.sub.S in accordance with the
following approximate range:
1.5.multidot..tau..sub.m/R.sub.S<(C.sub.A+C.sub.B)<2.7.multi-
dot..tau..sub.m/R.sub.S so as to be within approximately 1% of
optimal energy efficiency for a given .tau..sub.m and R.sub.S.
12. The method of claim 11, wherein the step of determining the
optimum values for the first and second capacitors, C.sub.A and
C.sub.B, comprises the step of: defining a relationship between
C.sub.A, C.sub.B and .tau..sub.m/R.sub.S in accordance with the
formula: C.sub.A=C.sub.B=.tau..sub.m/R.sub.S so as to result in the
minimum total stored energy needed for a given .tau..sub.m and
R.sub.S.
13. The method of claim 12, wherein the step of determining the
optimum values for the first and second capacitors, C.sub.A and
C.sub.B, comprises the step of: defining the relationship between
the first time constant, .tau..sub.S1, and the second time
constant, .tau..sub.S2, and the predetermined tissue time constant,
.tau..sub.m, by the formula
1/2.multidot..tau..sub.S1=2.multidot..tau..sub.S2=.tau..sub.m.
14. The method of claim 12, wherein the step of determining the
optimum duration for each time interval comprises the steps of:
defining the optimal duration for the first time interval as being
approximated by the formula:
d.sub.1.sup.opt=0.811.multidot..tau..sub.m; and defining the
optimal duration for the second time interval as being approximated
by the formula: d.sub.2.sup.opt=0.405.multidot..tau..sub.m.
15. The method of claim 13, wherein the step of determining the
optimum duration for each time interval comprises the steps of:
defining the optimum value for C.sub.A and C.sub.B approximately
equal to 60 .mu.F each; defining an approximate range of 2-4 ms
over which the tissue time constant, .tau..sub.m, may vary for any
given patient; defining an approximate range of 30-90 ohms over
which the tissue resistance, R.sub.S, may vary for any given
patient; defining an approximate range of 1.5 ms - 3.5 ms for the
optimal duration of the first time interval; and defining an
approximate range of 0.7 ms - 2.1 ms for the optimal duration of
the second time interval.
16. The method of claim 2, wherein the step of determining the
optimum duration for each time interval comprises the step of:
programming an approximate value for the predeteremined tissue time
constant, .tau..sub.m.
17. The method of claim 2, wherein the step of determining the
optimum duration for each time interval comprises the step of:
programming an approximate value for the predetermined tissue
resistance, R.sub.S.
18. The method of claim 2, wherein the step of determining the
optimum duration for each time interval comprises the step of:
measuring the tissue resistance, R.sub.S.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application claims the benefit of U.S. patent
application No. 09/073,394, filed May 5, 1998, which claims the
benefit of U.S. Provisional patent application No. 60/046,610,
filed May 14, 1997.
FIELD OF THE INVENTION
[0002] The present invention relates to implantable medical
devices, and more particularly to an implantable cardioverter
defibrillator (ICD) configured to provide a high efficiency
defibrillation waveform.
BACKGROUND OF THE INVENTION
[0003] An ICD continues to be a relatively large device for
implantation in the human body. The size of the ICD is primarily
determined by the battery and capacitors used therein. The size of
the battery (or batteries, in some instances) and capacitors, in
turn, is determined by the shock energy requirements for a
defibrillation pulse. Thus, a design approach which reduces the
energy requirements for defibrillation results in a direct
reduction in the overall ICD size.
[0004] In existing ICD devices, the defibrillation waveform or
pulse used to deliver a defibrillation shock to the heart is
generated by first charging the equivalent of a single capacitor
(most ICDs use two capacitors connected in series to function as a
single capacitor, thereby reducing the working voltage requirements
for each capacitor of the series stack, as explained below) to a
desired charge level (voltage) and then discharging the single
capacitor through the cardiac tissue for a prescribed period of
time during a first or positive phase of the defibrillation
waveform, and then reversing the polarity of the discharge for a
second prescribed period of time during a second or negative phase
of the defibrillation waveform, thereby producing a biphasic
stimulation pulse or waveform. It should be noted that in this
context the term "single capacitor" is used to refer to a single
capacitance, which may be, and usually is obtained by a hardwired
connection of two capacitors in series such that the two series
capacitors always function and act as though they were a single
capacitor. (Two capacitors are connected in series in this manner
in order to achieve a higher working voltage for the
series-connected capacitor. That is, when two capacitors are
connected in series, and each has a working voltage of, e.g., 375
volts (V), then the overall or total working voltage of the series
combination becomes 750 V.)
[0005] The purpose of applying a defibrillation shock to the heart
is to shock the heart out of a state of fibrillation, or other
non-functional state, into a functional state where it may operate
efficiently as a pump to pump blood through the body. To this end,
the positive phase of the biphasic waveform is preferably a very
high voltage that serves to synchronously capture as many heart
membrane cells as possible. See, Kroll, "A minimum model of the
signal capacitor biphasic waveform" Pace, November 1994. The
negative phase of the biphasic waveform, in contrast, simply serves
to remove the residual electrical charge from the membrane cells
and bring the collective membrane voltage back to its original
position or value. See, e.g., Kroll, supra; Walcott, et al.,
"Choosing The Optimal Monophasic and Biphasic Wave-Forms for
Ventricular Defibrillation,", Journal of Cardiovascular
Electrophysiology (September 1995). A biphasic pulse generator of
the type used in an ICD device is shown, e.g., in U.S. Pat. Nos.
4,850,357, issued to Bach, Jr.; and 5,083,562, issued to de
Coriolis et al.
[0006] When a voltage shock is first applied to a membrane cell,
the membrane does not respond to the shock immediately. Rather, the
cell response lags behind the applied voltage. This time lag is
more or less predictable in accordance with the Blair membrane
model. See, e.g., Blair, "On the intensity-time relations for
stimulation by electric currents. I" J. Gen Physiol., Vol. 15, pp.
709-729 (1932), and Blair, "On the intensity time relations for
stimulation by electric currents. II", J. Gen Physiol., Vol. 15,
pp. 731-755 (1932); Pearce et al., "Myocardial stimulation with
ultrashort duration current pulses," PACE, Vol. 5, pp. 52-58
(1982). When the applied voltage comprises a biphasic pulse having
a constant voltage level for the duration of the positive phase (a
condition achievable only when the voltage originates from an ideal
battery), the membrane cell response to the positive phase reaches
a peak (i.e., is at an optimum level) at the trailing edge of the
positive phase. Unfortunately, when the applied voltage originates
from a charged capacitor, as is the case for an ICD device, the
applied voltage waveform does not remain at a constant voltage
level, but rather has a significant "tilt" or discharge slope
associated therewith. Such tilt or slope causes the peak membrane
cell response to occur at some point prior to the trailing edge of
the positive phase, which is less than optimum. What is needed,
therefore, is a way to optimize the applied voltage waveform so
that a maximum membrane cell response occurs coincident with, or
nearly coincident with, the trailing edge of the positive
phase.
[0007] It is known in the art to switch the capacitors of an ICD
from a parallel configuration during the positive phase of a
biphasic defibrillation pulse to a series configuration during the
negative phase of the biphasic defibrillation pulse. See, e.g.,
U.S. Pat. Nos. 5,199,429 (FIG. 7A) and 5,411,525. While such action
produces a defibrillation waveform having a somewhat different
shape, i.e., a waveform having a leading edge voltage of the second
or negative phase which is approximately twice the trailing edge
voltage of the first or positive phase, such action does little to
achieve a maximum cell membrane response coincident with the
trailing edge of the first or positive phase.
[0008] It is also known in the art to sequentially switch
capacitors in an ICD device in order to allow waveform "tailoring",
e.g., prolong the positive phase duration by sequentially switching
in a second charged capacitor as shown in FIG. 9 of U.S. Pat. No.
5,199,429, or by sequentially switching in second, third and fourth
charged capacitors, as shown in FIG. 6C of U.S. Pat. No. 5,199,429.
However, such "tailoring" still does not address the main concern
of achieving a maximum cell membrane response coincident with the
trailing edge of the positive phase.
[0009] It is thus evident that what is needed is a capacitor
switching scheme and/or method for use within an ICD device which
achieves a maximum cell membrane response near or coincident with
the trailing edge of the positive phase.
[0010] It is also desirable to provide an ICD that is as small as
possible. The limiting factor on ICD thickness is the diameter of
the high-energy capacitors. As indicated above, current ICDs
typically use two electrolytic capacitors. Current technology in
electrolytic capacitors limits the stored voltage to about 370 V
per capacitor. Therefore, the current approach is to use two large
(.gtoreq.180 .mu.F) capacitors to achieve the stored energy of
.gtoreq.25J required for defibrillation. Therefore, the thickness
of the ICD is determined by the diameter of the large (.gtoreq.180
.mu.F) capacitors. There is thus a need for an ICD construction,
which would permit the needed energy for defibrillation to be
stored in the ICD, while allowing a thinner ICD thickness.
[0011] The present invention advantageously addresses the above and
other needs.
SUMMARY OF INVENTION
[0012] The present invention generates a highly efficient first
phase (which is usually a positive phase) of a biphasic
defibrillation pulse by switching at least two charged capacitors,
preferably three capacitors, from a parallel connection to a series
connection during the first or positive phase of the defibrillation
pulse. Such mid-stream parallel-to-series switch advantageously
steps up the voltage applied to the cardiac tissue during the first
phase. A stepped-up voltage during the first phase, in turn, gives
an extra boost to, and thereby forces additional charge (current)
into, the cardiac tissue cells, and thereby transfers more charge
into the membrane of the excitable cardiac cell than would be
transferred if the capacitors were continuously discharged in
series.
[0013] Phase reversal, e.g., switching to a second or negative
phase of the biphasic waveform) is timed to occur when the cell
membrane voltage reaches its maximum value at the end of the first
phase.
[0014] In accordance with one aspect of the invention, two
capacitors are used within the ICD to produce a two-step waveform
that outperforms the conventional one-step waveform. It will be
shown that the two-step waveform requires a 15.6% lower leading
edge, which may result in significantly less pain felt by the
patient, and further translates into at 28.8% reduction in required
stored energy. This reduction in leading edge amplitude and
required stored energy is achieved by controlling the durations of
the first and second steps in the two-step positive portion of the
waveform.
[0015] In accordance with another aspect of the invention, three
capacitors are used within the ICD in order to provide a thinner
ICD. These three capacitors store the same energy as a
two-capacitor ICD. These smaller capacitors have a smaller diameter
and therefore the ICD can be made thinner.
[0016] Disadvantageously, using three capacitors instead of two
creates its own set of problems that must be overcome by the
present invention. Using three capacitors discharged in series
results in: (a) high peak voltages (generally the peak voltage can
be three times 370 V or 1110 V); and (b) a small discharge time
constant, since the effective capacitance is that of a single
capacitor divided by three (or 40 .mu.F if 120 .mu.F capacitors are
used), resulting in a mismatch between the discharge (.tau.=R*C,
with R.apprxeq.50.OMEGA.) and tissue (.tau..sub.m.apprxeq.3 ms)
time constants. Advantageously, the present invention addresses
both of these concerns.
[0017] In accordance with another aspect of the invention, the
capacitors of the ICD are reconfigured from a parallel
configuration to a series configuration during the positive portion
of the defibrillation pulse. While this concept may be used
effectively with a two-capacitor ICD, it is preferred for purposes
of the present invention that at least three capacitors be used,
thereby allowing the ICD to be somewhat thinner that it otherwise
could be.
[0018] It is therefore a feature of the present invention to
provide an ICD that generates a highly efficient stimulation
waveform that transfers more charge to the membrane of an excitable
cardiac cell than has heretofore been possible using conventional,
series-discharge configurations.
[0019] It is a further feature of the invention to provide an ICD
design that results in a thinner ICD than has heretofore been
possible using a conventional two-capacitor ICDs.
BRIEF DESCRIPTION OF THE DRAWINGS
[0020] The above and other aspects, features, and advantages of the
present invention will be more apparent from the following more
particular description thereof, presented in conjunction with the
following drawings, wherein:
[0021] FIG. 1 illustrates a preferred defibrillation biphasic pulse
or waveform generated in accordance with a two-capacitor ICD in
accordance with the present invention;
[0022] FIG. 2 depicts the excitable cardiac membrane response to
the waveform of FIG. 1;
[0023] FIG. 3 is a functional block diagram of a two-capacitor ICD
device, which generates the waveform of FIG. 1;
[0024] FIG. 4 is a simplified schematic diagram of a
three-capacitor ICD made in accordance with the invention;
[0025] FIG. 5 illustrates one type of defibrillation waveform that
may be generated using the ICD of FIG. 4;
[0026] FIG. 6 depicts the excitable cardiac membrane response
during phase 1 (positive phase) to the waveform of FIG. 5;
[0027] FIG. 7 illustrates another type of defibrillation waveform
that may be generated using the ICD of FIG. 4;
[0028] FIG. 8 depicts the excitable cardiac membrane response
during phase 1 (positive phase) to the waveform of FIG. 7;
[0029] FIG. 9 illustrates, for comparative purposes, the biphasic
defibrillation waveform typically provided by a two-capacitor ICD
of the prior art;
[0030] FIG. 10 illustrates, again for comparative purposes, the
membrane response during phase 1 (positive phase) to the waveform
of FIG. 9.
[0031] FIG. 11 shows the first phase of a parallel/series discharge
waveform with the durations and time constants defined;
[0032] FIG. 12 shows a first contour plot of stored energy as a
function of a scaling factor "K" (equivalent to C.sub.A/C.sub.B and
the total capacitance (C.sub.A/C.sub.B as scaled by
.tau..sub.m/R.sub.S);
[0033] FIGS. 13 and 14 show a second and third contour plot of the
d.sub.1 and d.sub.2, respectively, as a function of the scaling
factor K and the total capacitance, wherein the optimal value
occurs at the cross-hair;
[0034] FIGS. 15, 16 and 17 illustrate how the optimal values for
d.sub.1 and d.sub.2, tissue resistance (R.sub.S) and tissue time
constants (.tau..sub.m);
[0035] FIG. 18 is a graph of optimal durations for d.sub.1 and
d.sub.2 as a function of tissue resistance (R.sub.S) for desired
(e.g., 60 .mu.F) capacitor and a range of tissue time constants
(.tau..sub.m);
[0036] FIG. 19 illustrates a single-step and a two-step
(parallel/series) waveform of equal stored energy and their
resulting cell membrane responses;
[0037] FIG. 20 illustrates the single-step and the two-step
waveforms normalized to achieve the maximum cell member response;
and
[0038] FIGS. 21 and 22 illustrate analogous results to those
depicted in FIG. 20 albeit for extreme combinations of R.sub.S and
C.sub.A (=C.sub.B).
DETAILED DESCRIPTION OF THE INVENTION
[0039] The following description is of the best mode currently
contemplated for practicing the invention.
[0040] The basic concept of the invention relating to forming an
efficient defibrillation waveform can be practiced with two or more
capacitors within the ICD. A preferred number of capacitors is
three. However, the basic concept will first be explained in the
context of a two-capacitor ICD.
[0041] In accordance with one aspect of the invention, then a
biphasic pulse or waveform is generated by an ICD device having two
capacitors that includes a positive phase of duration t.sub.1 ms
and a negative phase of duration t.sub.2 ms, as shown in FIG. 1.
First and second capacitors, C.sub.A and C.sub.B, within the ICD
device are initially charged to a voltage V.sub.1 and are connected
in parallel. The biphasic defibrillation pulse begins by
discharging the charged parallel capacitors through the cardiac
tissue by way of defibrillation electrodes in contact with the
cardiac tissue. Thus, a leading edge of the biphasic pulse starts
at a first peak voltage of approximately V.sub.1 volts (the charge
on the first and second capacitors when first connected to the
electrodes).
[0042] During a first portion of the positive phase of the biphasic
pulse, the amplitude of the biphasic pulse decays from the first
peak voltage V.sub.1 to a voltage V.sub.2 in accordance with a
first time constant .tau..sub.1. The first time constant
.tau..sub.1 varies as a function of (C.sub.A+C.sub.B)R, where
C.sub.A is the value of the first capacitor, C.sub.B is the value
of the second capacitor, and R is an effective resistance
associated with the discharge through the first and second
electrodes.
[0043] A second portion of the positive phase begins by connecting
the first and second capacitors in series. This sudden series
connection increases the defibrillation pulse to a second peak
voltage of approximately 2 (V.sub.2) volts (the sum of the voltages
on each of the first and second capacitors at the time the series
connection is made), as illustrated in FIG. 1. The amplitude of the
biphasic pulse decays during the second portion of the positive
phase from the second peak voltage 2 (V.sub.2) to a voltage V.sub.3
in accordance with a second time constant .tau..sub.2. The second
time constant .tau..sub.2 varies as a function of
(C.sub.AC.sub.B/C.sub.AC.sub.B) ) R. Advantageously, the voltage at
the trailing edge of the positive phase, V.sub.3, occurs at a time
that is near the maximum cell membrane response.
[0044] The negative phase of the biphasic waveform begins by
inverting the polarity of the series-connected first and second
capacitors. Such negative phase thus commences at a third peak
voltage of approximately -V3 volts, and decays thereafter towards
zero in accordance with the second time constant .tau..sub.2. After
a prescribed time period t.sub.2, the negative phase ends.
[0045] The biphasic waveform produced in accordance with the
two-capacitor ICD is illustrated in FIG. 1. The first portion of
the positive phase may terminate when either: (1) the voltage
decreases below a threshold voltage V.sub.3; or (2) a prescribed
time period t.sub.a has elapsed.
[0046] The tissue membrane voltage that results when the waveform
of FIG. 1 is applied to excitable cardiac tissue membranes is as
shown in FIG. 2. This membrane voltage is obtained by modeling the
tissue membranes as taught in the Blair reference, previously
cited. As shown in FIGS. 11-20, the optimum duration for t.sub.a
will be described in more detail.
[0047] A functional block diagram of the pulse generation circuitry
used to generate the biphasic waveform of the two-capacitor ICD is
shown in FIG. 3.
[0048] As seen in FIG. 3, a cardiac tissue-stimulating device 10
includes a power source 12, e.g., at least one battery, a timing
and control circuit 14, a charging circuit 16, an isolation switch
network SW1, a series parallel switch network SW2, at least two
capacitors C.sub.A and C.sub.B, an output switch network SW3, and
at least two electrodes 20 and 22. The electrodes 20 and 22 are
adapted to be positioned within or on the heart. The electrodes 20
and 22 are connected to the output switch SW3 through conventional
leads 21 and 23, respectively.
[0049] A voltage sense amplifier 24 senses the voltage held on the
capacitor C.sub.B (which will be the same voltage as capacitor
C.sub.A when C.sub.A and C.sub.B are connected in parallel). In
some embodiments of the invention, a current sense amplifier 26 may
also be used to sense the current flowing to or returning from one
of the electrodes 20 or 22. In FIG. 3, such current is sensed by
differentially measuring the voltage across a small current-sense
resistor R.sub.S connected in series with electrode 22. The outputs
of the voltage sense amplifier 24 and the current sense amplifier
26 are directed to the timing and control circuit 14.
[0050] A suitable cardiac activity sensor 28 is also employed
within the device 10 in order to detect cardiac activity. The
function of the sensor 28 is to sense cardiac activity so that an
assessment can be made by the timing and control circuitry whether
a defibrillation pulse needs to be generated and delivered to the
cardiac tissue. Such sensor 28 may take many forms, e.g, a simple
R-wave sense amplifier of the type commonly employed in implantable
pacemakers. The details of the sensor 28 are not important for
purposes of the present invention.
[0051] The power source 12 is connected to provide operating power
to all components and circuitry within the device 10. The power
source 12 also provides the energy needed to generate the biphasic
defibrillation pulse. That is, energy stored within the power
source 12 is used to charge capacitors C.sub.A and C.sub.B, through
the charging circuit 18, up to the desired initial defibrillation
starting pulse voltage V.sub.1. Such charging is carried out under
control of the timing and control circuit 14. Typically, V.sub.1
may be a relatively high voltage, e.g., 350 volts, even though the
power source 12 may only be able to provide a relatively low
voltage, e.g., 3-6 volts. The charging circuit 16 takes the
relatively low voltage from the power source 12 and steps it up to
the desired high voltage V.sub.1, using conventional voltage
step-up techniques as are known in the art. This stepped-up voltage
V.sub.1 is then applied through the isolation switch SW1 to both
capacitors C.sub.A and C.sub.B at a time when C.sub.A and C.sub.B
are connected in parallel, i.e., when SW2 is in its "P" position,
and at a time when the output switch is in its open, or OFF,
position. As the capacitors C.sub.A and C.sub.B are being charged,
the voltage sense amplifier 24 monitors the voltage level on the
capacitors. When the desired voltage V.sub.1 has been reached, the
timing and control circuitry 14 turns off the charging circuit 16
and opens the isolation switch SW1, thereby holding the voltage
V.sub.1 on capacitors C.sub.A and C.sub.B until such time as a
defibrillation pulse is needed.
[0052] When a defibrillation pulse is called for by the timing and
control circuit 14, the output switch SW3 is placed in its positive
phase position, POS, thereby connecting the parallel connected
capacitors C.sub.A and C.sub.B (on which the starting voltage
V.sub.1 resides) to the cardiac tissue through the electrodes 20
and 22. Such connection starts the discharge of capacitors C.sub.A
and C.sub.B through the cardiac tissue in accordance with the first
time constant .tau..sub.1 as described above in connection in FIG.
1.
[0053] After a period of time t.sub.a, or as soon as the voltage
across the parallel-connected capacitors C.sub.A and C.sub.B has
decreased to the threshold value V.sub.2 (as sensed by the voltage
sense amplifier 24), the timing and control circuit switches SW2 to
its series-connected or "S" position, thereby connecting the
capacitors C.sub.A and C.sub.B in series across the electrodes 20
and 22. Such series connection doubles the voltage across the
electrodes 20 and 22 to a value of 2(V.sub.2) Thereafter, the
discharge of the series-connected capacitors C.sub.A and C.sub.B
continues through the cardiac tissue in accordance with the second
time constant .tau.2 as described above. This discharge continues
until the end of the positive phase.
[0054] The positive or first phase ends at a time t.sub.1 from the
beginning of the positive phase (as measured by timing circuits
within the timing and control circuit 14), or when the voltage has
decayed to a value V.sub.3 (as sensed by voltage sense amplifier
24). Alternatively, the positive phase may end as a function of the
sensed current (as sensed by the current sense amplifier 26), e.g.,
at a time when the sensed current has decreased from a peak value
by a prescribed amount or percentage.
[0055] As soon as the positive phase ends, the timing and control
circuit 14 switches the output switch SW3 to the negative phase
position, NEG, thereby reversing the polarity of the discharge of
the series-connected capacitors C.sub.A and C.sub.B through the
cardiac tissue. The negative phase lasts thereafter for a time
period t.sub.2 determined by the timing and control circuitry.
[0056] The functions represented by the functional block diagram of
FIG. 3 may be implemented by those of skill in the art using a wide
variety of circuit elements and components. It is not intended that
the present invention be directed to a specific circuit, device or
method; but rather that any circuit, device or method which
implements the functions described above in connection with FIG. 3
to produce a defibrillation waveform of the general type shown in
FIG. 1 be covered by the invention.
[0057] Turning next to FIG. 4, there is shown a simplified
schematic diagram of an ICD having three 120 .mu.F capacitors C1,
C2 and C3. The manner of charging the capacitors while they are
connected in parallel is the same or similar to that shown in FIG.
3. When the capacitors C1, C2 and C3 have been charged to a high
voltage, e.g., 370 V, a stored energy of approximately 25 Joules is
realized. Once the capacitors have been charged by the ICD, the
capacitors are configured for a parallel discharge. This is
accomplished by closing switches S1, S2, S3 and S4, while
maintaining switches S5 and S6 open. The parallel discharge takes
place from time t=0 until a time d.sub.1. Once d.sub.1 elapses, one
of two options may be used to discharge the remaining charge.
[0058] In accordance with a first option, or Option 1, after
d.sub.1 has elapsed (i.e., after the capacitors are discharged in
parallel until time d.sub.1), all of the capacitors are discharged
in series for the remainder of the pulse. This is accomplished by
opening S1, S2, S3 and S4 and closing S5 and S6. At a later time,
d.sub.2, the "H Bridge" circuit 40 (FIG. 4) is used to reverse the
polarity of the output. At yet a later time, d, the output pulse is
truncated.
[0059] The waveform generated in accordance with Option 1 is
illustrated in FIG. 5. The tissue membrane voltage associated with
the waveform of FIG. 5 is modeled and computed, using the Blair
model, as shown in FIG. 6. For the example shown in FIGS. 5 and 6,
the optimum value of d.sub.1 is nominally about 3.5 ms. The optimum
choice of d.sub.2 is when the elapsed time at d.sub.2 is about 1.5
times the elapsed time at d.sub.1, or when the elapsed time at
d.sub.2 (from t=0) is about 5.25 ms.
[0060] In accordance with a second option, or Option 2, the
capacitors C1 and C2 remain in parallel and are in series with C3
until time d.sub.2. This is accomplished by opening S3 and S4 and
closing S6. After d.sub.2 all the capacitors are in series (S1 and
S2 also open, 55 closed) until C3 runs out of charge at a time
d.sub.4. After d.sub.4, the diode D.sub.1 bypasses the depleted
capacitor and the time constant of discharge is of C1 and C2 in
series. At a time d.sub.3, where d.sub.2<d.sub.3<d.sub- .4,
the polarity of the output is reversed using the H Bridge 40. The
pulse is truncated at time d. The resulting waveform is shown in
FIG. 7. The resulting membrane voltage is modeled and computed and
shown in FIG. 8.
[0061] For the example shown in FIGS. 7 and 8, the optimum values
of d, is 2.7 ms, d.sub.2 is 1.5 times d.sub.1 (or about 4 ms) ,
d.sub.3 is d.sub.2+1.25 ms. The value of d.sub.4 is computed to be
about 7.6 ms. The choice of d can be in the range of 1.5 to 2.0
times that of d.sub.3.
[0062] With either Option 1 or Option 2, the choice of the values
d.sub.1, d.sub.2 and d.sub.3 are primarily functions of the ICD's
capacitance value, the discharge pathway impedance, and the tissue
time constant (.tau..sub.m).
[0063] The advantage of Option 2 is that the peak waveform voltage
is lower than Option 1 yet a minute increase in membrane voltage
over Option 1 is achieved. However, Option 1 is simpler to
implement and diode D.sub.1 is not needed since all the capacitors
are discharged equally.
[0064] The advantages of either Option 1 or Option 2 are better
appreciated by comparing the results of such discharge, as
presented in FIGS. 5, 6, 7 and 8, with the corresponding discharge
achieved with a two-capacitor ICD series discharge, as is commonly
used in a conventional ICD of the prior art. The discharge waveform
achieved with a conventional two-capacitor ICD using series
discharge, and the resulting membrane voltage, is shown in FIGS. 9
and 10, respectively. Note, that to store equal energy to the three
capacitor ICD, each capacitor of the two-capacitor ICD must have
1.5 times the capacitance value, or two capacitors each with C=180
.mu.F.
[0065] As can be seen from a comparison of FIGS. 9 and 10 with
FIGS. 5 and 6 (Option 1), and 5A and 5B (Option 2), for equal
stored energy, the value of the peak membrane voltage for Option 2
is 1.18 times higher than the membrane voltage realized using the
conventional waveform. Similarly, Option 1 yields a membrane
voltage that is 1.17 times higher than is realized using the
conventional waveform. In other words, a 25 Joule ICD with three
120.mu.F capacitors and a switching network as in Option 2 performs
equally to a 34.4 Joule conventional ICD with two 180.mu.F
capacitors. This represents a remarkable improvement in
performance.
[0066] As shown in FIG. 11, the two-step waveform has been
reproduced. Although identical in nature to that shown in FIG. 1,
the designators have been changed slightly for purposes of the in
depth analysis that will follow.
[0067] As described above in conjunction with FIG. 3, two
capacitors, C.sub.A & C.sub.B, have been charged to the same
initial voltage, V.sub.01. The system resistance (as seen by
device) is given by R.sub.S. For purposes of this discussion, the
myocardium has been modeled as a parallel-RC circuit with
myocardial tissue time constant, .tau..sub.m.
[0068] The amplitude of each step of the positive portion of the
defibrillation waveform, shown in FIG. 11, can be characterized
with the following basic equations:
V.sub.S1(t.sub.1)=V.sub.01.multidot.exp[-t.sub.1/.tau..sub.S1]
0.ltoreq.t.sub.1.ltoreq.d.sub.1
V.sub.S2(t.sub.2)=V.sub.02.multidot.exp[-t.sub.2/.tau..sub.2]
0.ltoreq.t.sub.2.ltoreq.d.sub.2
[0069] wherein:
[0070] V.sub.S1 is the exponential decay during the first period,
t.sub.1, (i.e., Step1);
[0071] V.sub.S2 is the exponential decay during the second period,
t.sub.2, (i.e., Step2);
[0072] .tau..sub.S1 is the time constant of C.sub.A and C.sub.B in
parallel;
[0073] .tau..sub.S2 is the time constant of C.sub.A and C.sub.B in
series;
[0074] V.sub.01 is the initial voltage during Step1 on the
capacitors C.sub.A and C.sub.B once fully charged to the source
voltage, V.sub.01; and
[0075] V.sub.02 is the initial voltage during Step2 remaining on
the capacitors C.sub.A and C.sub.B now configured in series.
[0076] The analysis that follows directly will explain how to
determine the absolute and approximate solutions for the optimal
durations, d.sub.1 and d.sub.2, to maximize induced myocardial
potential, V.sub.m(t), when the two capacitors are arranged in a
parallel-series, two-step arrangement.
[0077] Consider the myocardial responses to V.sub.S1(t.sub.1)
[Step1] and V.sub.S2(t.sub.2) [Step2] separately. Note that the
following derivations (Equations 1-4) make absolutely no
assumptions regarding any specific relationships between the
characteristics of Step1 and Step2.
[0078] The "Step1" myocardial response, V.sub.m1, to the Step1
waveform, V.sub.s1, is described by: 1 V m1 ( t 1 ) t 1 + V m1 ( t
1 ) m V s1 ( t 1 ) m (Eq. 1)
[0079] with the initial condition: V.sub.m1(0)=0.
[0080] The solution to this differential equation is: 2 V m1 ( t 1
) = { V 01 1 ( exp [ - t 1 s1 ] - exp [ - t 1 m ] ) s1 m V 01 s1 (
t 1 exp [ - t 1 s1 ] ) s1 = m where 1 = 1 - ( m / s1 ) . (Eq.
2)
[0081] The "Step2" myocardial response, V.sub.m2, to the Step2
waveform, V.sub.s2, is governed by: 3 V m2 ( d 1 , t 2 ) t 2 + V m2
( d 1 , t 2 ) m V s2 ( t 2 ) m (Eq. 3)
[0082] with the initial condition:
V.sub.m2(d.sub.1,0)=V.sub.m1(d.sub.1), where d.sub.1 represents the
final duration of Step1.
[0083] This initial condition ensures that there is a continuity of
myocardial voltage when transitioning from the end of Step1 into
the start of Step2. The solution to this differential equation is:
4 V m2 ( d 1 , t 2 ) = V m1 ( d 1 ) exp [ - t 2 m ] + { V 02 ( d 1
) 2 ( exp [ - t 2 s2 ] - exp [ - t 2 m ] ) s2 m V 02 ( d 1 ) s2 ( t
1 exp [ - t 2 s2 ] ) s2 = m (Eq. 4)
[0084] where .alpha..sub.2=1-(.tau..sub.m/.tau..sub.s2), and
V.sub.02 is proportional to V.sub.S2(0)
[0085] Equation (4) describes a curve with a single maximum value.
The step durations, d.sub.1=d.sub.1.sup.opt and
d.sub.2=d.sub.2.sup.opt, that maximize this shock-induced
myocardial voltage, V.sub.m2(t.sub.1, t.sub.2) can be determined by
solving the simultaneous equations given by: 5 V m2 ( d 1 opt , d 2
opt ) d 1 opt = 0 V m2 ( d 1 opt , d 2 opt ) d 2 opt = 0 (Eq.
5)
[0086] From Equation (5), two equations that describe
d.sub.2.sup.opt as a function of d.sub.1.sup.opt can be found (the
following derivations assume .tau..sub.s1.tau..sub.m and
.tau..sub.s2.tau..sub.m): 6 d 2 opt = m 2 ln { 1 + ( 2 1 V 01 V 02
/ d 1 opt ) ( 1 s1 exp [ - d 1 opt s1 ] - 1 m exp [ - d 1 opt m ] )
} (Eq. 6) 7 d 2 opt = m 2 ln { t 2 m [ 1 - ( 2 1 V 01 V 02 ( d 1
opt ) ) ( exp [ - d 1 opt s1 ] - exp [ - d 1 opt m ] ) ] } (Eq.
7)
[0087] Setting Equations (6) and (7) equal to each other and
simplifying produces the following implicit equation for
d.sub.1.sup.opt: 8 ( m s2 1 V 01 ) = ( 1 / s1 V 02 / d 1 opt + s2 /
m V 02 ( d 1 opt ) ) exp [ - d 1 opt s1 ] - ( 1 / m V 02 / d 1 opt
+ s2 / m V 02 ( d 1 opt ) ) exp [ - d 1 opt m ] (Eq. 8)
[0088] Further simplifications of Equation (8) require that
V.sub.02(d.sub.1) be explicitly defined.
[0089] When the two system capacitors (C.sub.A & C.sub.B) are
configured into a parallel arrangement during Step1 and then
reconfigured into a series arrangement during Step2, the system
time constants can be explicitly defined as:
.tau..sub.S1=R.sub.S.multidot.(C.sub.A+C.sub.B)
.tau..sub.s2=R.sub.S.multi- dot.(C.sub.AC.sub.B)/(C.sub.A+C.sub.B)
(Eq. 9)
[0090] Furthermore, V.sub.02(d.sub.1) is explicitly defined as:
V.sub.02(d.sub.1)=2.multidot.V.sub.s1(d.sub.1)
=2.multidot.V.sub.01.multid- ot.exp[-d.sub.1/.tau..sub.s1] (Eq.
10)
[0091] where Equation (10) codifies the notion that, in a
parallel-series arrangement, the leading edge voltage of Step2
equals twice the trailing edge voltage of Step1.
[0092] Substituting Equation (10) into Equation (8) and solving
explicitly for d.sub.1.sup.opt and subsequently d.sub.2.sup.opt
[via Equation (6) or (7)] yields: 9 d 1 opt = - m 1 ln { ( m s1 ) (
2 1 - 2 1 - 2 ) } (Eq. 11) d 2 opt = + m 1 ln { ( 1 2 ) ( 2 1 - 2 1
- 2 ) } (Eq. 12)
[0093] The maximum myocardial voltage attained using these optimal
parallel-series step durations can then be determined by
substituting Equations (10)-(12) into Equation (4) and simplifying:
10 V m2 ( d 1 opt , d 2 opt ) = V 01 ( 1 2 ) - 1 2 ( m s1 ) 1 1 - 1
( 2 1 - 2 1 - 2 ) 1 1 - 1 2 (Eq. 13)
[0094] Note that Equations (11)-(13) are valid for any independent
values of C.sub.A and C.sub.B.
[0095] According to this simple RC model of defibrillation,
successful defibrillation is achieved when the myocardial voltage
(as embodied herein by V.sub.m1 and V.sub.m2) is "depolarized" to
its threshold value, V.sub.th. An equation that describes the
minimum relative magnitude for V.sub.0 (i.e., the voltage to which
each of the capacitors is charged in preparation for the
defibrillation shock) that successfully drives V.sub.m2 to V.sub.th
can be obtained from Equation (13) by setting V.sub.m2=V.sub.th and
solving for V.sub.01 (which, for these parallel-series shocks, is
equivalent to V.sub.0).
[0096] Since the total stored energy in capacitors C.sub.A and
C.sub.B is given by: 11 E stored = 1 2 ( C A + C B ) V 0 2 (Eq.
14)
[0097] then the optimal relationship between C.sub.A and C.sub.B
that maximizes myocardial voltage for a given total stored energy
can be found by substituting C.sub.A=k.multidot.C.sub.B into
Equation (14) and then solving for k in
.differential.E.sub.stored/.differential.k=9. The result is:
k.sup.opt=C.sub.A/C.sub.B=1 (Eq. 15)
[0098] The above result implies that C.sub.A should equal C.sub.B
in order to achieve maximum myocardial impact for any given total
energy. The relationship C.sub.A=C.sub.B is equivalent to
.tau..sub.s1=4.multidot..ta- u..sub.s2 [see Equation (9)], from
which simplified versions of Equations (1l)-(13) can be derived: 12
d 1 opt = m 1 ln { ( 1 3 ) ( 1 + m 2 s2 ) } (Eq. 16) d 2 opt = + m
2 ln { ( 1 3 ) ( 1 + 2 s2 m ) } (Eq. 17) V m2 ( d 1 opt , d 2 opt )
= 2 V 01 ( m 2 s2 ) 1 2 - 1 [ ( 1 3 ) ( 1 + m 2 s2 ) ] 1 1 - 1 2
(Eq. 18)
[0099] Finally, the optimal capacitance for a given R.sub.S and
.tau..sub.m is determined by finding the value of C.sub.A that
minimizes E.sub.stored, that is, solving for C.sub.A in
.differential.E.sub.stored/- .differential.C.sub.A=0 (with k=1).
The result is: 13 C A = C B = m R s (Eq. 19)
[0100] or equivalently, the optimal capacitance (for a given
R.sub.S and .tau..sub.m) is that which satisfies: 14 1 2 s1 = 2 s2
= m ( Eq . 20 )
[0101] Under these ideal conditions, the optimal step durations
are:
d.sub.1.sup.opt=+2.tau..sub.m.multidot.1n[3/2]
.apprxeq.0.811.multidot..ta- u..sub.m (Eq. 21)
d.sub.2.sup.opt=+.tau..sub.m.multidot.1n[3/2]
.apprxeq.0.405.multidot..tau- ..sub.m (Eq. 22)
[0102] Further insights into the preceding theoretical calculations
can be gleaned from corresponding graphical analyses. The relative
stored energy required for defibrillation (E.sub.stored) for all
possible parallel-series two-step waveforms is graphically
illustrated in the contour plot of FIG. 12. In this plot, the
x-axis is indexed by the total capacitance (C.sub.A+C.sub.B, scaled
by .tau..sub.m/R.sub.S) while the y-axis is indexed by the ratio of
the two capacitances (k=C.sub.A/C.sub.B). Although perhaps
seemingly non-intuitive axis definitions, they efficiently provide
complete coverage of the entire parameter space of all possible
capacitor combinations for two-step waveforms. As indicated by the
horizontal line 100 and the vertical line 102 overlaid on this plot
(and as consistent with the conclusions of Equations (15) and
(19)), the most efficient two-step positive portion for the
biphasic shock is delivered when:
k=1.0; and
C.sub.A+C.sub.B=2.multidot..tau..sub.m/R.sub.S;
[0103] which occurs at point 104 in FIG. 12.
[0104] The contours then step out from this optimal point in 1%
increments, thus providing an indication as to the relative
sensitivity of the energy efficiency to deviations in either total
capacitance or capacitance ratio. In fact, energy efficiency
remains quite robust: for example, energy efficiency remains within
1% of optimal for:
.about.1.5.multidot..tau..sub.m/R.sub.S<(C.sub.A+C.sub.B)<.about.2.7-
.multidot..tau..sub.m/R.sub.S; and
.sup.180.7<k<.sup.18 1.4.
[0105] Two-dimensional contour plots of optimal Step1 and Step2
durations (normalized by .tau..sub.m, i.e.,
d.sub.1.sup.opt/.tau..sub.m and d.sub.2.sup.opt/.tau..sub.m) as
given by Equations (11) and (12) are presented in FIGS. 13 and 14,
respectively.
[0106] Similar to FIG. 12, FIGS. 13 and 14 have respective
horizontal lines 110, 120 and vertical lines 112, 122 from have
been overlaid on these contour maps as well. Their respective
intersections 114, 124 appropriately correspond to the "0.811" and
"0.405" coefficients found in Equations (21) and (22),
respectively.
[0107] Since R.sub.S and .tau..sub.m represent patient-specific
variables that directly impact the choice of durations used for
these stepped waveforms, it is perhaps useful to present example
values for d.sub.1.sup.opt and d.sub.2.sup.opt for a representative
range of values for R.sub.S (30-90 .OMEGA.), .tau..sub.m (2-4 ms),
and C.sub.A (30-90 .mu.F). The tables shown in FIGS. 15-17 provide
such a set of example values, wherein values for d.sub.1.sup.opt
and d.sub.2.sup.optare computed from Equations (16) and (17),
respectively.
[0108] Given the limits of the ranges used for R.sub.S,
.tau..sub.m, and C.sub.A in the tables shown in FIGS. 15-17,
d.sub.1.sup.opt and d.sub.2.sup.opt range from lows of 1.286 and
0.422 ms (when .tau..sub.m=2 ms, C.sub.A=30 .mu.F, and R.sub.S=30
.OMEGA.) to highs of 3.704 and 2.689 ms (when .tau..sub.m=4 ms,
C.sub.A=90 .mu.F, and R.sub.S=90 .OMEGA.), respectively.
[0109] To summarize the above, for the ranges of:
.tau..sub.m=2-4 ms;
R.sub.S=30-90 .OMEGA.;
C.sub.A=C.sub.B=30-90 .mu.F
[0110] Then, the optimum durations fall in the ranges:
d.sub.1.sup.opt=1.286-3.704
d.sub.2.sup.opt=0.422-2.689
[0111] Of course, d.sub.1.sup.opt and/or d.sub.2.sup.opt could move
outside of these ranges if any one or more of R.sub.S, .tau..sub.m,
and C.sub.A exceed the limits used for these tables. In those
cases, Equations (16) and (17) could be used to compute exactly the
optimal step durations for any combination of R.sub.S, .tau..sub.m
and C.sub.A.
[0112] In another embodiment, the device could also determine
d.sub.1.sup.opt and d.sub.2.sup.opt based on measured values for
R.sub.S, and/or a programmed value for .tau..sub.m based on a
particular value for C.sub.A and C.sub.B.
[0113] By way of example, if the capacitance value for C.sub.A and
C.sub.B is set to 60 .mu.F, so that Equation 19 is satisfied for a
tissue resistance, R.sub.S equal to nominally 50 ohms and a tissue
time constant, .tau..sub.m, then for a range for .tau..sub.m, of 2
ms to 4 ms, and a range for R.sub.S of 30-90 ohms, then:
[0114] If .tau..sub.m=2.0 ms and Rs=90 ohms, then:
C.sub.A+C.sub.B)*R.sub.s/.tau..sub.m=5.4
d.sub.1.sup.opt=0.962 * .tau..sub.m(=1.923 ms)
d.sub.2.sup.opt=0.809 * .tau..sub.m(=1.618 ms)
[0115] If .tau..sub.m=4.0 ms and Rs=30 ohms, then:
(C.sub.A+C.sub.B)*R.sub.S/.tau..sub.m=0.9
d.sub.1.sup.opt=0.643 * .tau..sub.m (=2.573 ms)
d.sub.2.sup.opt=0.211 * .tau..sub.m (=0.844 ms)
[0116] To further assist with interpreting the results embodied in
FIGS. 13 and 14 and the table shown in FIGS. 15-17, FIG. 18 graphs
a subset of those data as simple functions of R.sub.S and
.tau..sub.m. In particular, FIG. 18 presents a pair of graphs: the
left and right halves plot d.sub.1.sup.opt and d.sub.2.sup.opt,
respectively, as functions of R.sub.S for three representative
values of .tau..sub.m (2, 3, and 4 ms). For these graphs,
C.sub.A=C.sub.B=60 .mu.F (thus k=1.0). Consistent with the data in
the tables shown in FIGS. 15-17 both d.sub.1.sup.opt and
d.sub.2.sup.opt increase in value with increasing R.sub.S or
.tau..sub.m. Moreover, this figure helps illustrate how
d.sub.1.sup.opt appears significantly more sensitive to relative
changes in .tau..sub.m than in R.sub.S, while d.sub.2.sup.opt
appears to have the opposite sensitivity.
[0117] While FIGS. 12-17 provide a comprehensive overview of all
possible parallel-series two-step waveforms, it is also useful to
consider some specific examples that can aid in illustrating the
relative improvements gained by using such a parallel-series
two-step capacitor arrangement over the traditional one-step
arrangement.
[0118] FIG. 19 graphically compares the positive portion of the
biphasic shock waveform shapes (V.sub.S, top two waveforms, 150 and
160) and associated tissue responses (V.sub.m, bottom two
waveforms, 152 and 162) for one-step, 150, and parallel-series
two-step, 160, shocks having equal stored energies and leading-edge
voltages.
[0119] For this example, shown in FIG. 19:
[0120] .tau..sub.m=3 ms, R.sub.S=50 .OMEGA., C.sub.A=C.sub.B=60
.mu.F
[0121] (thus, Equations 15 & 19 are satisfied).
[0122] The one-step shock is generated by essentially keeping
C.sub.A and C.sub.B in a parallel arrangement for its entire shock
duration, for a constant effective capacitance of 120 .mu.F. As is
evident from the tissue responses (i.e., comparing the one-step
response 152 to the two-step response 162), two-step the myocardial
voltage (162) reaches a higher higher final cell membrane potential
(+18.6%) in a shorter total duration (3.65 vs. 4.16 ms 12.3%) as
compared to the final cell membrane potential (152) using the
one-step shock. A consequence of this improved tissue response is
that this two-step waveform requires a lower effective leading-edge
voltage (and hence a lower stored energy) to achieve the same
defibrillation efficacy as its equivalent one-step waveform.
[0123] FIG. 20 illustrates this scenario by resealing the results
presented in FIG. 19 such that the strength of each shock is
sufficient to produce tissue responses of equal amplitudes.
Consistent with the results presented in FIG. 19, this two-step
positive portion of the biphasic shock waveform 164 theoretically
requires a 15.6% lower leading-edge voltage than its one-step
counterpart 154, which translates into a 28.8% reduction in
required stored energy, and a potentially lower pain waveform for
the patient since the leading edge of the shocking pulse is
reduced.
[0124] FIGS. 21 and 22 illustrate analogous results to those
depicted in FIG. 20, but for relatively extreme combinations of
R.sub.S and C.sub.A. In FIG. 21, R.sub.S=30 .OMEGA. and C.sub.A
=C.sub.B=30 .mu.F, while in FIG. 22, R.sub.S=90 .OMEGA. and
C.sub.A=C.sub.B=90 .mu.F. As is evident in FIGS. 21 and 22, the
shape of the optimal parallel-series two-step waveform depends
strongly on the magnitudes of R.sub.S and C.sub.A. Furthermore, the
relative improvement in energy efficiency also strongly depends on
these values.
[0125] For example, in FIG. 21, the two-step waveform 166 induced
an equivalent final tissue response as its one-step waveform 156,
but with an 8.8% shorter duration (2.1 vs. 2.3 ms), a 6.5% lower
leading-edge voltage, and a 12.6% reduction in required stored
energy.
[0126] In FIG. 22, the relative improvements were a 14.3% shorter
duration (5.3 vs. 6.3 ms), a 25.9% lower leading-edge voltage, and
a 45.0% reduction in required stored energy. Thus, these
comparisons suggest that there would be especially great incentive
for utilizing two-step waveforms instead of traditional one-step
waveforms when the magnitudes of R.sub.S and C.sub.A are large,
while the incentive is relatively minimal when the magnitudes of
R.sub.S and C.sub.A are small. Unfortunately, because of the
inherent limitations of this theoretical model, it is not possible
to directly compare amplitude-based results (e.g., leading-edge
voltage, required stored energy) derived for differing R.sub.S or
.tau..sub.m. For this reason, the results of FIGS. 20-22 are all
self-normalized (that is, there is no relationship between the
amplitudes in these graphs).
[0127] Finally, while Equations (16) and (17) provide exact
formulas for determining d.sub.1.sup.opt and d.sub.2.sup.opt when
k=1 (i.e. , C.sub.A=C.sub.B) , it is sometimes helpful and/or
practical to also identify various approximations to such
solutions. Consider the following infinite series expansion of the
natural logarithm: 15 ln [ x ] = 2 [ ( x - 1 x + 1 ) + 1 3 ( x - 1
x + 1 ) 3 + 1 5 ( x - 1 x + 1 ) 5 + ] ( 23 )
[0128] Utilizing just the first term of this expansion, Equations
(16) and (17) can be simplified to: 16 d 1 opt 2 m 3 - 1 = 2 s1 m 2
s1 + m 1 d 1 opt 1 2 s1 + 1 m = 1 4 R s C A + 1 m ( 24 ) d 2 opt 2
m 3 - 2 2 = s2 2 m s2 + 2 m 1 d 2 opt 1 s2 + 1 2 m = 1 2 ( 4 R s C
A + 1 m ) ( 25 )
[0129] In words, these relationships suggest that the optimal step
durations can be well approximated by computing variously weighted
parallel combinations of system and myocardial time constants. And
despite using only one term of Equation (23), these approximations
are relatively quite accurate over a broad range of
.tau..sub.S1/.tau..sub.m and .tau..sub.S2/.tau..sub.m ratios (only
their ratios, not their absolute values, impact their accuracy).
For example, the relative error for d.sub.1.sup.opt is less than 5%
for 0.4<.tau..sub.S1/.tau..sub.m&l- t;5, while the relative
error for d.sub.2.sup.opt is less than 5% for
0.2<.tau..sub.S2/.tau..sub.m<3. When Equation (20) is also
satisfied (that is, when system and myocardial time constants are
ideally matched), these relative errors are each only 1.35%. In all
cases, these approximation calculations underestimate the true
values by these respective relative errors.
[0130] While the invention herein disclosed has been described by
means of specific embodiments and applications thereof, numerous
modifications and variations could be made thereto by those skilled
in the art without departing from the scope of the invention set
forth in the claims.
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